The length of a rectangle is 5 times its width decreased by 2. If the perimeter is 308 inches,
what is the length and width of the rectangle?
L = 5W-2
2L + 2W = 2(5W-2) + 2W = 10W-4 + 2W = 308
Solve for W then L.
To find the length and width of the rectangle, we can set up two equations based on the given information.
Let's say the width of the rectangle is 'w' inches.
According to the problem, the length of the rectangle is 5 times its width decreased by 2. So, the length can be represented as 5w - 2.
Now, let's set up the equations based on the given information:
1. Perimeter equation:
The perimeter of a rectangle is given by the formula: Perimeter = 2(length + width)
In this case, the perimeter is given as 308 inches, so we can write:
308 = 2(5w - 2 + w)
2. Length equation:
The length of the rectangle is given as 5 times its width decreased by 2:
Length = 5w - 2
Now we can solve these equations to find the values of 'w' and the corresponding length '5w - 2'.
Let's solve the first equation:
308 = 2(5w - 2 + w)
308 = 2(6w - 2)
308 = 12w - 4
12w = 312
w = 26
Now substitute the value of 'w' back into the length equation:
Length = 5w - 2
Length = 5(26) - 2
Length = 130 - 2
Length = 128
Therefore, the length of the rectangle is 128 inches and the width is 26 inches.